Allen Air Conditioning manufactures room air conditioners at plants in Houston, Phoenix, and Memphis. These are sent to regional distributors in Dallas, Atlanta, and Denver. The shipping costs vary, and the company would like to find the least-cost way to meet the demands at each of the distribution centers. Dallas needs to receive 800 air conditioners per month, Atlanta needs 600, and Denver needs 200. Houston has 850 air conditioners available each month, Phoenix has 650, and Memphis has 300. The shipping cost per unit from Houston to Dallas is $8, to Atlanta $12, and to Denver $10. The cost per unit from Phoenix to Dallas is $10, to Atlanta $14, and to Denver $9. The cost per unit from Memphis to Dallas is $11, to Atlanta $8, and to Denver $12. Required:
a. How many units should owner Stephen Allen ship from each plant to each regional distribution center?
b. What is the total transportation cost?

$14700

Explanation:

Given that:

i. Dallas needs 800 per month

ii. Atlanta needs 600 per month

iii. Denver needs 200 per month

iv. Houston has 850 available per month

v. Phoenix has 650 available per month

vi. Memphis has 300 available per month

Assuming that a plant can deliver air conditioners to more than one regional distributor in a month. Then;

a. For least-cost way to meet the demand, Stephen Allen could ship the air conditioners to each regional distributors as follows:

From Houston to Dallas = 800 units

From Houston to Atlanta = 50 units

From Phoenix to Atlanta = 250 units

From Memphis to Atlanta = 300 units

From Phoenix to Denver = 200 units

Total units transported = 1600 units

b. Cost per transportation:

Houston to Dallas = $8 x 800  = $6400

Houston to Atlanta = $12 x 50 = $600

Phoenix to Atlanta = $14 x 250 = $3500

Memphis to Atlanta = $8 x 300 = $2400

Phoenix to Denver = $9 x 200 = $1800

Total transportation cost = $6400 +$600 + $3500 + $2400 + $1800

                                         = $14700

The total transportation cost would be $14700.